Material #1. r θ x Material #2. Material #1

Transcription

1 I T y Maerial Adherend T d c r θ x Maerial Adhesive T Maerial Adherend T I Fig. 1. A crack wihin he adhesive layer in an adhesive bond. The adherend is designaed as maerial 1 and adhesive is designaed as maerial 2. The coordinae sysem is se a he crack ip. 62

2 12.5 mm 3 ~ 4 Direcion of crack propagaion Fig. 2. The cross-secion of he failed specimen wih T = 35 MPa and alernaing crack rajecory. The picure on he righ is he scanning elecron microscopy (SEM) micrograph of he circled porion of he crosssecion. 63

3 y L x R Fig. 3. The idealized crack rajecory geomery used in references 1 and 2. 64

4 P a Inerfacial crack /2 P a 0 k Transverse crack Fig. 4. A double canilever beam (DCB) specimen wih simplified crack rajecory for direcionally unsable crack propagaion. 65

5 y z σ σ δ(y) Adhesive E2 H Adherend E 1 B Fig. 5. The geomery and he sress sae of a ransverse crack in he DCB specimen wih simplified crack rajecory for direcionally unsable crack propagaion. 66

6 σ r = 13 MPa, ε p =1.3% σ r = 13 MPa, ε p =1.1% σ r = 13 MPa, ε p =0.65% σ r = 13 MPa, ε p = σ r = 0, ε p = Adherend Thickness - H [mm] Fig. 6. Available srain energy release rae for direcionally unsable crack propagaion in DCB specimen wih various condiions. Normalized Srain Energy Release Rae Sable Unsable 2 67

7 I I y y H H r r θ x θ x K 1 + ik δ 2 + i I I I (a) (b) Fig. 7. Cracks in a DCB specimen: a) inerfacial crack; b) cohesive crack. The specimen is under exernal, and I loading, which can also be described as far field sress inensiy facors. 68

8 I [MPa(mm) 1/2 ] G = 155 J/m 2 G = 310 J/m 2 G = 620 J/m 2 δ/ y r θ x δ Fig. 8. The curve of local mode II sress inensiy facor I versus he non-dimensional locaion of he sub-inerfacial crack varies wih he applied srain energy level. 69

9 Al/Epoxy Al 2 O 3 /Ti Cu/Al 2 O 3 y r δ θ x I [MPa(mm) 1/2 ] δ/ Al/Epoxy Al 2 O 3 /Ti µ 1 GPa µ 2 GPa ν 1 ν 2 α β Cu/Al 2 O Fig. 9. Parameric sudy of he local mode II sress inensiy facor I versus he non-dimensional locaion of he sub-inerfacial crack for differen maerial combinaions. 70

10 M Adherend T T M Adherend Adhesive Crack perurbaion Iniial inerfacial crack Fig. 10. The finie elemen mesh for predicing he crack rajecory in DCB specimen using Franc2dl. 71

11 + i I 350 a S J-Inegral - J [J/m 2 ] Along he inerface Terminaes a he inerface Ino adhesive Ino adherend Normalized crack lengh S/ Fig. 11. Srain energy release rae (J-inegral value) available a he crack ip versus he non-dimensional crack lengh obained using he finie elemen analysis. 72

12 Phase angle - ψ [degree] Terminaes a he inerface H + i I S a Normalized crack lengh S/ Fig. 12. Phase angle a he crack ip versus he non-dimensional crack lengh obained by he finie elemen analysis. 73

13 5 Phase Angle - ψ [degree] L/ L -15 Fig. 13. Phase angle a he crack ip versus he non-dimensional inerfacial crack lengh obained by he finie elemen analysis. 74

14 3 ~ 4 M Adherend Leave inerface gradually T Š Slope increasing 3.5 Adhesive M Abrup kink near inerface Adherend Fig. 14. The crack rajecory prediced by he finie elemen analysis using Franc2dl. The resul reflecs he overall characerisics of he acual crack rajecory such as he characerisic lengh of he crack as shown in he SEM micrograph. 75